In fact, there is a wide variety of recent applications of \(U(1)_{\mu -\tau }\)  models, which
are distinguished by additional particle contents to address flavor anomalies; Refs [1]}, [2]}, [3]}, [4]}, [5]}, [6]} for neutrino oscillations to control lepton flavor structure, Refs [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]} for muon \(g-2\) , Refs [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]} for
\(b \rightarrow s \mu ^+ \mu ^-\)  anomalies, and (or) DM. Qualitative features in \(U(1)_{\mu -\tau }\)  models for flavor anomalies are the following.
The muon \(g-2\)  anomaly is explained by light \(Z^{\prime }\)  around \(\mathcal {O}(10)\)  to \(\mathcal {O}(100)\)  MeV scale or by Yukawa interactions with exotic fermions controlled by \(U(1)_{\mu - \tau }\)  symmetry.
For explaining \(b \rightarrow s \mu ^+ \mu ^-\)  anomalies with \(U(1)_{\mu -\tau }\) , generally we need to add new particles since the corresponding gauge boson \(Z^{\prime }\)  does not couple to quarks.
Mixing among the SM quarks and new vector-like quarks are considered to generate flavor violating \(Z^{\prime }\) -quark coupling in refs [22]}, [21]}, [26]} while flavor dependent charge assignment in the SM quark sector is considered in ref. [23]}.
